The sign for spider is a natural sign, resembling a spider crawling around. You sign spider by crossing your open hands at the wrist. Wiggle your fingers around, as if they're the legs of a spider, and at the same time, move your hands to make the spider move forward.
Spider is a useful sign for intermediate signer. Start by teaching babies the general sign (bug), then move on to the more specific signs like spider, bee, and ant. Moving from general to specific - as your baby gets more advanced with her signing and starts to be able to distinguish the differences between bugs - helps your baby develop her vocabulary and keeps signing challenging.
We use spider when we sing, "Itsy, Bitsy Spider". We also like to use it when reading story books about spiders.